function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
%   theta = GRADIENTDESCENT(X, y, theta, alpha, num_iters) updates theta by 
%   taking num_iters gradient steps with learning rate alpha

% Initialize some useful values
m = length(y); % number of training examples
J_history = zeros(num_iters, 1);


for iter = 1:num_iters

    % ====================== YOUR CODE HERE ======================
    % Instructions: Perform a single gradient step on the parameter vector
    %               theta. 
    %
    % Hint: While debugging, it can be useful to print out the values
    %       of the cost function (computeCost) and gradient here.
    %
    temp1 = 0.0;
    temp2 = 0.0;
    for j = 1:m,
        temp1 = temp1 + (X(j, :)*theta - y(j)) * X(j, 1);
        temp2 = temp2 + (X(j, :)*theta - y(j)) * X(j, 2);
    end;
    
    theta(1) = theta(1) - alpha*temp1 / m;
    theta(2) = theta(2) - alpha*temp2 / m;
    
    % ============================================================

    % Save the cost J in every iteration    
    J_history(iter) = computeCost(X, y, theta);

end
